Entanglement and Correlation Spreading in non-Hermitian Spin Chains

Turkeshi, Xhek; Schiró, Marco

doi:10.48550/arxiv.2201.09895

Cited by 4 publications

(4 citation statements)

References 55 publications

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“…On the other hand, the result for finite ratio /N is a conjecture inspired by the zero-temperature CFT scaling [21]. Similar logarithmic terms as in (3) have been found in a tight-binding model, although for different nonequilibrium settings [33][34][35][36][37]. Finally, the last term O( 1) is a subleading constant, which can be calculated, at least for the tight-binding chain, by using the Fisher-Hartwig conjecture [38][39][40][41][42][43].…”

Section: Introductionsupporting

confidence: 66%

Logarithmic entanglement scaling in dissipative free-fermion systems

2022

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We study the quantum information spreading in one-dimensional free-fermion systems in the presence of localized thermal baths. We employ a nonlocal Lindblad master equation to describe the system-bath interaction, in the sense that the Lindblad operators are written in terms of the Bogoliubov operators of the closed system, and hence are nonlocal in space. The statistical ensemble describing the steady state is written in terms of a convex combination of the Fermi-Dirac distributions of the baths. Due to the singularity of the free-fermion dispersion, the steady-state mutual information exhibits singularities as a function of the system parameters. While the mutual information generically satisfies an area law, at the singular points it exhibits logarithmic scaling as a function of subsystem size. By employing the Fisher-Hartwig theorem, we derive the prefactor of the logarithmic scaling, which depends on the parameters of the baths and plays the role of an effective "central charge." This is upper bounded by the central charge governing ground-state entanglement scaling. We provide numerical checks of our results in the paradigmatic tight-binding chain and the Kitaev chain.

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Section: Introductionsupporting

confidence: 66%

Logarithmic entanglement scaling in dissipative free-fermion systems

2022

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“…Later studies show the entanglement transitions also appear in more generalized non-unitary random evolutions [19][20][21][22][23][24]. In particular, in free-fermion systems, under non-unitary random evolution, there is a stable critical phase, in which the steady state has power-law correlation functions and logarithmic entanglement entropy, with possible entanglement transitions into area-law phases [18,[25][26][27][28][29][30][31][32][33][34][35]. This criticality is attributed to the existence of Goldstone modes from the spontaneous breaking of the continuous symmetry in the enlarged replicated Hilbert space [18,28,29].…”

Section: Introductionmentioning

confidence: 99%

Universal Entanglement Transitions of Free Fermions with Long-range Non-unitary Dynamics

Zhang

Liu

Jian

et al. 2022

Quantum

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Non-unitary evolution can give rise to novel steady states classified by their entanglement properties. In this work, we aim to understand the effect of long-range hopping that decays with r−α in non-Hermitian free-fermion systems. We first study two solvable Brownian models with long-range non-unitary dynamics: a large-N SYK2 chain and a single-flavor fermion chain and we show that they share the same phase diagram. When α>0.5, we observe two critical phases with subvolume entanglement scaling: (i) α>1.5, a logarithmic phase with dynamical exponent z=1 and logarithmic subsystem entanglement, and (ii) 0.5<α<1.5, a fractal phase with z=2α−12 and subsystem entanglement SA∝LA1−z, where LA is the length of the subsystem A. These two phases cannot be distinguished by the purification dynamics, in which the entropy always decays as L/T. We then confirm that the results are also valid for the static SYK2 chain, indicating the phase diagram is universal for general free-fermion systems. We also discuss phase diagrams in higher dimensions and the implication in measurement-induced phase transitions.

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“…shown that the entanglement dynamics of monitored free fermions display a subtle behavior, with transitions and crossovers between phases with sub-extensive scaling [30,32,[35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54]. This phenomenon was quantitatively understood only very recently, exploiting a mapping to effective non-linear-sigma-model field theories [34,[55][56][57], see also [33].…”

Section: Introductionmentioning

confidence: 99%